Considering things like potions, ethers, antidotes, etc, exist, I think there is most definitely medicine in Eorzea other than white magic. The Phrontistery (Alchemists' Guild) has many rooms with beds where people are treated with alchemical medicines, rather than magical means. It's likely a 'if one doesn't work try the other' situation or it could be determined by whether the person has access to a magical healer, money for treatment, etc.
There are definitely things that magic and medicine cannot heal in Eorzea as well, as evident by a small group of NPCs outside the conjurers' guild discussing the passing of a child that couldn't be saved by them. There's mentions of a plague that decimated the Hyur population as well (a cure has been found). Even with magic and medicine, Eorzeans are still quite mortal!
I'm sorry I can't provide you with more specifics without the game being up! x_x
There are definitely things that magic and medicine cannot heal in Eorzea as well, as evident by a small group of NPCs outside the conjurers' guild discussing the passing of a child that couldn't be saved by them. There's mentions of a plague that decimated the Hyur population as well (a cure has been found). Even with magic and medicine, Eorzeans are still quite mortal!
I'm sorry I can't provide you with more specifics without the game being up! x_x
